Cahn-Hilliard Hydrodynamics and Topological Transitions

                             by

          John Lowengrub, School of Math, U. Minn.

          JTB 320, 3:20pm  Thursday, January 30, 1997

                          Abstract

 The competition between surface tension and instability
 often leads to singularities in interfacial flows in which
 interfaces collide and/or self-intersect and the topology
 of the flow changes. Before the singularity, sharp
 interface models provide good models of the flow. At the
 singularity time, however, these models break down and
 additional features of the flow must be considered such as
 the partial miscibility between ``immiscible'' fluid
 components.

 In this talk, I will introduce a new model (Cahn-Hilliard
 Hydrodynamics) in which sharp interfaces are replaced by
 microscopic mixing layers that account for the partial
 miscibility that real fluids always display. Analysis and
 simulations will demonstrate the model's ability to capture
 changes in topology.

Requests for preprints and reprints to: rmm@math.utah.edu